This invention relates to a diffraction lens and the method of designing the same, in particular, to a diffraction lens having a diffraction relief on a lens surface and the method of designing the diffraction lens.
For a diffraction lens, it has been heretofore known a lens which has a diffraction relief for generating diffraction on a lens surface. For example, in respect of a diffraction lens for use in an optical pick up device, an achromatic objective lens and a two-focus objective lens which utilize the characteristics peculiar to diffraction have been proposed.
The shape of the lens surface of these diffraction lenses is optimized by a method of adding an optical path difference function on the virtual basic aspherical surface or basic spherical surface by the high refractive index method or phase function method, and after that, it is transformed into the actual shape of a diffraction relief having steps from the optical path difference function.
The positions of the steps in the direction perpendicular to the optical axis can be obtained as the height such that the optical path difference function varies by an amount of an integral number times the wavelength, and the amount of variation in the direction of the optical axis is approximated by a function form in order to be easily treated. For example, in the publication of TOKKAIHEI 10-186231, it is disclosed that the amount of displacement in a diffraction relief and the amount of displacement in a basic aspherical surface with a diffraction relief added are approximated by a polynomial with a distance from the optical axis made as a variable.
However, the above-described method of approximation using a polynomial has a problem that the working of diffraction lenses is likely to become complicated because of the large number of the terms in the function [form].
This invention has been done in view of it that the respective surfaces of the diffraction annular zones can be approximated as surfaces formed by rotation around the respective predetermined points on the virtual basic aspherical surface or basic spherical surface, and an object of this invention is to provide the method of designing a diffraction lens wherein a high-precision approximate shape can be obtained by a simple expression in the process of transformation from the optical path difference function to the actual shape of a diffraction relief having steps. Further, another object of this invention is to provide a diffraction lens which has a diffraction relief with a simple shape and is made by a high-precision expression.
The above-described objects can be accomplished by any one of the following structures and methods:
1. A diffractive lens, comprises
an optical axis;
a lens surface having a peripheral portion, and
a diffractive relief provided on the lens surface,
wherein the diffractive relief is shaped in annular zones, and
wherein following conditional formulas (1) and (2) are satisfied:
hixe2x88x921xe2x89xa6h less than hixe2x80x83xe2x80x83(1)
x=f(hxe2x88x92hti)+Sxe2x80x83xe2x80x83(2)
xe2x80x83where
i is a suffix showing an ordinal number of each of the diffractive annular zones obtained by counting each diffractive annular zone in such a manner that a diffractive annular zone including the optical axis is counted as a first diffractive annular zone and other diffractive annular zones are counted respectively in consecutive order from the optical axis toward the peripheral portion;
h is a distance between a point and X axis in which, when the optical axis is deemed as X axis, the distance is from X axis to the point in a direction perpendicular to X axis;
hi is a distance from X axis to a border between i-th diffractive annular zone and (i+1)-th diffractive annular zone which are counted from the optical axis in the above manner, provided that h0=0;
f(h) is a function of h;
hti is a constant in which at least one of hti is not zero; and
S is a term characterizing an aspherical surface.
It may be preferable that S is zero, because a highly precise diffractive lens may be produced more easily.
2. The diffractive lens described in paragraph 1, wherein f(h) is a following conditional formula (3):                               f          ⁡                      (                          h              -                              h                ti                                      )                          =                                                                              (                                      h                    -                                          h                      ti                                                        )                                2                            /                              r                ti                                                    1              +                                                1                  -                                                                                    (                                                  h                          -                                                      h                            ti                                                                          )                                            2                                        /                                          r                      ti                      2                                                                                                    +                      x            ti                    -                      r            ti                                              (        3        )            
xe2x80x83where rti is a constant and xti is a constant.
3. The diffractive lens described in paragraph 1, wherein the diffractive relief is shaped in a sawtooth.
4. The diffractive lens described in paragraph 3, wherein a difference in a direction parallel to the optical axis between a cross sectional shape of the diffractive relief and a shape represented by a following general formula (4) is not larger than 0.2 of a basic wavelength:                                           x            ⁡                          (              h              )                                =                                                                                          Φ                    D                                    ⁡                                      (                    h                    )                                                  ⁢                                  xe2x80x83                                ⁢                cos                ⁢                                  xe2x80x83                                ⁢                θ                                            cos                ⁢                                  xe2x80x83                                ⁢                α                ⁢                                  xe2x80x83                                ⁢                                  {                                      n                    -                                                                  n                        xe2x80x2                                            ⁢                      cos                      ⁢                                              xe2x80x83                                            ⁢                                              (                                                  θ                          -                                                      θ                            xe2x80x2                                                                          )                                                                              }                                                      +                                          x                B                            ⁡                              (                h                )                                                    ⁢                  xe2x80x83                                    (        4        )            
xe2x80x83where
xB(h) represents a shape of a basic aspherical surface or a basic spherical surface;
"PHgr"D(h) represents an optical path difference produced by providing the diffractive relief on the lens surface;
xcex8 is an angle made between a ray, which comes from an object point on the optical axis and is incident on a diffractive surface, and a normal line on the diffractive surface.;
xcex8xe2x80x2 is an angle made betwee a ray, which comes from the object point on the optical axis and emerges from the diffraction surface, and a normal line on the diffractive surface;
xcex1 is an angle made between the optical axis and a normal line on the diffractive surface;
n is a refractive index of the incident side of the diffractive surface; and
nxe2x80x2 is a refractive index of the emerging side of the diffractive surface.
5. A method of manufacturing a mold to produce a diffractive lens having a diffractive relief on a lens surface, comprises steps of:
inputting data regarding a shape of the diffractive relief into a computer provided to a mold processing machine; and
processing a metal block by the mold processing machine controlled by the computer based on the inputted data
so that the mold to produce the diffractive lens is manufactured,
wherein the data are represented by following conditional formulas (1) and (2):
hixe2x88x921xe2x89xa6h less than hixe2x80x83xe2x80x83(1)
x=f(hxe2x88x92hti)xe2x80x83xe2x80x83(2)
xe2x80x83where
i is a suffix showing an ordinal number of each of the diffractive annular zones obtained by counting each diffractive annular zone in such a manner that a diffractive annular zone including the optical axis is counted as a first diffractive annular zone and other diffractive annular zones are counted respectively in consecutive order from the optical axis toward the peripheral portion;
h is a distance between a point and X axis in which, when the optical axis is deemed as X axis, the distance is from X axis to the point in a direction perpendicular to X axis;
hi is a distance from X axis to a border between i-th diffractive annular zone and (i+1)-th diffractive annular zone which are counted from the optical axis in the above manner, provided that h0=0;
f(h) is a function of h; and
hti is a constant in which at least one of hti is not zero.
6. A method of producing a diffractive lens having a diffractive relief on a lens surface, comprises steps of:
inputting data regarding a shape of the diffractive relief into a computer provided to a mold processing machine;
processing a metal block by the mold processing machine controlled by the computer based on the inputted data
so that the mold to produce the diffractive lens is manufactured, and
producing the diffractive lens by injecting molding a melted plastic with use of the mold;
wherein the data are represented by following conditional formulas (1) and (2):
hixe2x88x921xe2x89xa6h less than hixe2x80x83xe2x80x83(1)
x=f(hxe2x88x92hti)xe2x80x83xe2x80x83(2)
xe2x80x83where
i is a suffix showing an ordinal number of each of the diffractive annular zones obtained by counting each diffractive annular zone in such a manner that a diffractive annular zone including the optical axis is counted as a first diffractive annular zone and other diffractive annular zones are counted respectively in consecutive order from the optical axis toward the peripheral portion;
h is a distance between a point and X axis in which, when the optical axis is deemed as X axis, the distance is from X axis to the point in a direction perpendicular to X axis;
hi is a distance from X axis to a border between i-th diffractive annular zone and (i+1)-th diffractive annular zone which are counted from the optical axis in the above manner, provided that h0=0;
f(h) is a function of h; and
hti is a constant in which at least one of hti is not zero.
7. A method of designing a diffractive lens having a diffractive relief on a lens surface, wherein the diffractive relief is shaped in annular zones, comprises steps of:
designing the diffractive lens so as to satisfy following conditional formulas (1) and (2):
hixe2x88x921xe2x89xa6h less than hixe2x80x83xe2x80x83(1)
x=f(hxe2x88x92hti)xe2x80x83xe2x80x83(2)
xe2x80x83where
i is a suffix showing an ordinal number of each of the diffractive annular zones obtained by counting each diffractive annular zone in such a manner that a diffractive annular zone including the optical axis is counted as a first diffractive annular zone and other diffractive annular zones are counted respectively in consecutive order from the optical axis toward the peripheral portion;
h is a distance between a point and X axis in which, when the optical axis is deemed as X axis, the distance is from X axis to the point in a direction perpendicular to X axis;
hi is a distance from X axis to a border between i-th diffractive annular zone and (i+1)-th diffractive annular zone which are counted from the optical axis in the above manner, provided that h0=0;
f(h) is a function of h; and
hti is a constant in which at least one of hti is not zero.
Further, the above-described objects may be accomplished by any one of the following preferable structures:
8. A diffraction lens having a diffraction relief on a lens surface, wherein the optical axis of said diffraction lens is let to be the x-axis, h is let to be the distance from said optical axis in the direction perpendicular to said optical axis, and assuming that h falls within the range expressed by the inequality (1) described below, the shape of a diffraction relief on at least one lens surface is expressed by the following equation (2):
hixe2x88x921xe2x89xa6h less than hixe2x80x83xe2x80x83(1)
x=f(hxe2x88x92hti)xe2x80x83xe2x80x83(2)
xe2x80x83where i, hi, f(h), and hti have meanings described below:
i: a suffix showing the ordinal number of the diffraction annular zones obtained by counting the diffraction annular zones in consecutive order from the diffraction annular zone of the diffraction relief including the optical axis, which is made the first annular zone, toward the circumference;
hi: the distance of the border between the ith diffraction annular zone and the (i+1)th diffraction annular zone from the optical axis, where h0=0;
f(h): a function of h; and
hti: a constant with i made a suffix, where at least one of hti is not zero.
9. A diffraction lens having a diffraction relief on a lens surface, wherein the optical axis of said diffraction lens is let to be the x-axis, h is let to be the distance from said optical axis in the direction perpendicular to said optical axis, and assuming that h falls within the range expressed by the inequality (1) described below, the shape of a diffraction relief on at least one lens surface is expressed by the following equation (2xe2x80x2):
hixe2x88x921xe2x89xa6h less than hixe2x80x83xe2x80x83(1)
x=f(hxe2x88x92hti)+Sxe2x80x83xe2x80x83(2xe2x80x2)
xe2x80x83where i, hi, f(h), hti, and S have meanings described below:
i: a suffix showing the ordinal number of the diffraction annular zones obtained by counting the diffraction annular zones in consecutive order from the diffraction annular zone of the diffraction relief including the optical axis, which is made the first annular zone, toward the circumference;
hi: the distance of the border between the ith diffraction annular zone and the (i+1)th diffraction annular zone from the optical axis, where h0=0;
f(h): a function of h;
hti: a constant as i made a suffix, where at least one of hti is not zero; and
S: a term characterizing an aspherical surface.
10. The diffraction lens set forth in the above-described paragraph 8 or 9, wherein the expression of the aforesaid function of h f(h) is the below-described expression (M3):
xe2x80x83(M3)                               f          ⁡                      (                          h              -                              h                ti                                      )                          =                                                                              (                                      h                    -                                          h                      ti                                                        )                                2                            /                              r                ti                                                    1              +                                                1                  -                                                                                    (                                                  h                          -                                                      h                            ti                                                                          )                                            2                                        /                                          r                      ti                      2                                                                                                    +                      x            ti                    -                      r            ti                                              (        3        )            
xe2x80x83where rti and xti have meanings described in the following:
rti: a constant having i as a suffix; and
xti: a constant having i as a suffix.
11. The diffraction lens set forth the above-described paragraphs 8, 9, or 10, which is designed by a method of adding an optical path difference function onto the virtual basic aspherical surface or basic spherical surface and has a diffraction relief composed of diffraction annular zones having a sawtooth cross-sectional shape in the plane including the optical axis, wherein the deviation in the direction parallel to the optical axis between said cross-sectional shape of the diffraction relief and the shape expressed by the below-described expression M4 is equal to or smaller than one fifth of the standard wavelength:
xe2x80x83(M4)                                           x            ⁡                          (              h              )                                =                                                                                          Φ                    D                                    ⁡                                      (                    h                    )                                                  ⁢                                  xe2x80x83                                ⁢                cos                ⁢                                  xe2x80x83                                ⁢                θ                                            cos                ⁢                                  xe2x80x83                                ⁢                α                ⁢                                  xe2x80x83                                ⁢                                  {                                      n                    -                                                                  n                        xe2x80x2                                            ⁢                      cos                      ⁢                                              xe2x80x83                                            ⁢                                              (                                                  θ                          -                                                      θ                            xe2x80x2                                                                          )                                                                              }                                                      +                                          x                B                            ⁡                              (                h                )                                                    ⁢                  xe2x80x83                                    (        4        )            
xe2x80x83where xB(h), "PHgr"D(h), xcex8, xcex8xe2x80x2, xcex1, n, and nxe2x80x2 have meanings described in the following:
xB(h): the shape of the basic aspherical surface or basic spherical surface;
"PHgr"D(h): the optical path difference produced by providing a diffraction relief on the lens surface;
xcex8: the angle made by a ray which comes from an object point on the optical axis and is incident on the diffraction surface and the normal to said diffraction surface;
xcex8xe2x80x2: the angle made by a ray which comes from an object point on the optical axis and emerges from the diffraction surface and the normal to said diffraction surface;
xcex1: the angle made by the optical axis and the normal to the diffraction surface;
n: the refractive index of the incident side of the diffraction surface; and
nxe2x80x2: the refractive index of the emerging side of the diffraction surface.
12. A method of designing a diffraction lens having a diffraction relief on a lens surface, wherein the optical axis of said diffraction lens is let to be the x-axis, h is let to be the distance from said optical axis in the direction perpendicular to said optical axis, and assuming that h falls within the range expressed by the inequality (1) described below, the shape of a diffraction relief on at least one lens surface is expressed by the following equation (2):
hixe2x88x921xe2x89xa6h less than hixe2x80x83xe2x80x83(1)
x=f(hxe2x88x92hti)xe2x80x83xe2x80x83(2)
xe2x80x83where i, hi, f(h), and hti have meanings described below:
i: a suffix showing the ordinal number of the diffraction annular zones obtained by counting the diffraction annular zones in consecutive order from the diffraction annular zone of the diffraction relief including the optical axis, which is made the first annular zone, toward the circumference;
hi: the distance of the border between the ith diffraction annular zone and the (i+1)th diffraction annular zone from the optical axis, where h0=0;
f(h): a function of h; and
hti: a constant with i made a suffix, where at least one of hti is not zero.